Group Graphing – Grade Four Lesson Summary:

Group Graphing – Grade Four  Lesson Summary:
Group Graphing – Grade Four
Ohio Standards
Connection
Data Analysis and
Probability
Benchmark C
Construct charts, tables and
graphs to represent data,
including picture graphs,
bar graphs, line graphs,
line plots and Venn
diagrams.
Indicators
2. Represent and interpret
data using tables, bar
graphs, line plots and
line graphs.
4.
Compare different
representations of the
same data to evaluate
how well each
representation shows
important aspects of
the data, and identify
appropriate ways to
display the data.
Mathematical Processes
Benchmarks
I. Represent problem
situations in a variety
of forms (physical
model, diagram, in
words or symbols),
and recognize when
some ways of
representing a problem
may be more helpful
than others.
K. Use mathematical
language to explain
and justify
mathematical ideas,
strategies, and
solutions.
Lesson Summary:
Students in small groups create survey questions, collect data
on the questions, organize the data into tables, and generate
several types of graphs (including bar, line, and picture) to
represent the data. During the post assessment, groups
interpret each other’s graphs, as well as evaluate the best type
of graph to represent the data collected from their own group
survey.
Estimated Duration: Three hours
Commentary:
Understanding the limitation of graphs is important, as well as
understanding the types of graphs suitable for different types of
data. Students must have opportunities to analyze and discuss
the purposes and limitations of different kinds of graphs.
Providing negative examples of graphs and allowing students to
explore the problems with those graphs is as necessary as
seeing proper examples of graphs.
Pre-Assessment:
 Collect graphs from newspapers, magazines or textbook
resources. Make a transparency of each graph.
 Show students a pictograph, bar graph and a line graph on the
overhead projector.
 Ask students to write down the type of graph (pictograph, bar
or line). Then, ask students one or two questions connected to
each graph. The questions should ask students to identify how
many or how much of something is represented in the graph
or to identify when or where the most or least occurred.
1. How is the data represented in this graph?
2. What interval is used on the graph?
 Conduct a discussion about the information available in bar,
line and picture graphs.
Scoring Guidelines:
During the class discussion of the graphs, make informal
anecdotal records of the students’ understanding. Focus on
whether or not the students know the different types of graphs.
Also, note if students can read and interpret the different graphs.
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Group Graphing – Grade Four
Post-Assessment:
This post-assessment is a continuation of the groups’ work in the main lesson beginning with
step 10.
 Have students look at the three types of graphs (bar, line and picture) they have created to
represent their collection of data.
 Have students work individually to decide which of the three types of graph best represents
the data, and have students write a response explaining why that type of graph best represents
the data.
 Have each student also write an explanation of why one of the other graphs does NOT
represent the data well.
Provide a group of students with another group’s set of interpretation questions to answer in a
written form. Students answer these questions individually.
Scoring Guidelines:
Use Selection of Best Graph Post-Assessment Rubric, Attachment A, to assess what students
know about how each type of graph.
Instructional Procedures:
Part One
1. Use Three Untitled Graphs, Attachment B, showing only the graphs in the left column, and
lead a discussion about how data is represented by a variety of graphs. Discuss how some
types of graphs are more appropriate for different types of data, the audience for the results
and the purpose in reporting the results. Use some of these guiding questions:
 What can you tell me about these graphs? (types, missing titles, missing axis labels)
 What are some questions that might apply to these graphs?
 What are some advantages/disadvantages when using each type?
 Which of these could show the average high temperatures in Columbus?
 Which of these could show the answer to the question posed to a class of third graders,
“What is the most common day to be absent?”
 Which type of graph could show the answer to the question, “How many brothers and
sisters do you have?”
2. Uncover the graphs in the right column (cover the top portion) and continue the discussion:
 How are these graphs different than the ones just shown? (axis labels and graph titles are
provided)
 What are some additional questions that could apply to these graphs?
 How do the axis labels help the reader interpret information?
 What does a picture graph need that the other two do not have? (key indicating value of
each picture)
 Why is a key important to a picture graph?
 The line graph is not a good choice for representing data concerning the number of
student absences. Why? (There is no meaning for points on the line between the days of
the week. A scatter plot would be a better choice.)
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Group Graphing – Grade Four

3.
4.
5.
6.
What other kinds of data would not be appropriate for a line graph? (Any data that falls
into categories, where there is not meaning for between categories. Some examples are
colors of jackets worn in the winter, homeroom teacher of students, types of cars owned
by families, pets, etc.)
Present the following scenario.
Mary wants to invite ten friends to her birthday party and asks them what flavor of ice cream
they would like to have at the party. Four of her friends like chocolate, two friends prefer
strawberry, one enjoys mint chocolate chip, and three like cookie dough.
a. Ask students which kind of graph they would choose to represent this data and give a
reason why they would choose that type.
b. Have the students help create the graph on the chalkboard or overhead.
c. Have students make up questions relating to the graph. (Which type of ice cream should
Mary order the largest amount of? How many more friends liked chocolate more than
strawberry? Which flavor is the least favorite? )
Present the following situation to the students:
Gary planted a bean seed. He kept track of how many inches tall his plant grew. Here is his
list: week 1, 2 inches; week 2, 5 inches; week 3, 6 inches; and week 4, 8 inches.
a. Ask students which kind of graph they would choose to represent this data and give a
reason why they would choose that type.
b. Have the students help create the graph on the chalkboard or overhead.
c. Have students make up questions relating to the graph.
Inform the students know that they will be placed in small groups during the next lesson to
complete a task which includes determining a survey question, collecting data, organizing the
data into a table, representing the data in at least three different graphic forms and creating
interpretation questions for their graphs.
For homework, have students make a list of possible survey questions for the small group to
consider during the next lesson.
Instructional Tip:
Make clear to the students that this survey question must be able to be answered immediately,
not requiring any further research or questioning to answer.
7. Have students respond to the following prompt in writing in their mathematics journals or
use Learning about Types of Graphs, Attachment C. Discuss the importance of titles and axis
labels for graphs. Also, explain what you know or have learned about the three different
types of graphs: bar, line and picture.
Instructional Tip:
Read the students’ journal entries before the next class period to see if any further discussion of
the three types of graphs is needed.
Part Two
8. Have several students share their journal entries from the previous day.
9. Place the students into small groups of three to five students. Allow the small groups to share
their survey questions from the homework assignment.
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Group Graphing – Grade Four
10. Interrupt the sharing after about five minutes and lead a class discussion about making the
survey questions interesting. This will assist the students in creating a wide variety of
questions, rather than the typical “What is your favorite (color, food, pizza topping, etc.)?”
a. Tell the groups that they have five minutes to decide upon their group’s survey question.
b. As the groups select their question, write them on the board. If a question is already on
the board, it may not be used a second time. This ensures no repetition of survey
questions. The question also is written at the top of a class list at the group’s table.
Instructional Tips:
 Having a class list of names available helps each group know if someone did not answer the
survey question. The students place their answers to the questions beside their own name.
 If the class has a small number of students, consider building in a little extra time to survey
another class as well.
c. Take approximately 15 minutes to have all students circulate among the small-group
tables answering the different survey questions. The class list with the survey question
written on it remains at the group’s table while the students move around answering
questions.
d. When all groups are finished collecting data, they begin the task of organizing it into
charts, representing it by creating three different graphs (bar, line and picture), and
creating three to four interpretation questions about the set of completed graphs. These
are displayed on chart paper to make them large enough to be seen easily when posted
around the room.
e. Use the rest of the math class to begin work on the charts and graphs.
11. Have the groups complete the Exit Card, Attachment D, which lists the tasks the group has
completed. Have each student complete a card, but turn them in as a small group.
Instructional Tip:
Looking over the cards will help plan how much time to provide to finish the lesson. It may take
an extra day.
Part Three
12. Have the students sit in their small groups from Part Two of the lesson. Return the exit cards
from the previous day to remind students what still needs to be done.
13. Circulate among groups assisting where needed.
14. As groups finish their charts, graphs and questions, post them on the walls around the room
to be used during the post-assessment.
Instructional Tip:
Check through the interpretation questions created by each group to ensure that they are
appropriate for use in the post-assessment.
15. When the groups are finished with their work, have them answer the following selfreflection questions in their journals:
a. How well did my group work together?
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Group Graphing – Grade Four
b. How could my group improve?
c. How did I contribute to the group?
d. What new information did I learn about bar graphs? line graphs? picture graphs?
16. After all groups are finished, the students will be using the group graphs and interpretation
questions to complete the Post-assessment activities.
Differentiated Instructional Support:
Instruction is differentiated according to learner needs, to help all learners either meet the intent
of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified
indicator(s).
 Provide pre-made forms to create the graphs. These would have blank lines for axis labels
and for the title, and, possibly, even the intervals preset.
 If students are having difficulties with creating questions, provide example interpretation
questions for them to use when creating the ones for their own graphs.
 Have them investigate and use other types of graphs and plots (e.g., circle, double bar, double
line graphs.)
 Have them survey different populations (e.g. kindergarten or fifth-grade students,
teacher/staff members, etc.) with the same survey questions. Then, have them create a second
set of graphs, interpret the similarities/differences between population responses, and finally,
conjecture why those similarities or differences occurred.
Extension:
Encourage students to use their graphing skills to communicate information about your school to
others. Examples of such communication could be the variety of lunch menu items throughout
the month/year or how many days of absence occur each month. These graphs could then be
shared through the daily morning announcements (if they are televised) or the school newspaper.
Home Connection:
Collect real-life examples of graphs from newspapers, magazines, brochures, etc.
Materials and Resources:
The inclusion of a specific resource in any lesson formulated by the Ohio Department of
Education should not be interpreted as an endorsement of that particular resource, or any of its
contents, by the Ohio Department of Education. The Ohio Department of Education does not
endorse any particular resource. The Web addresses listed are for a given site’s main page,
therefore, it may be necessary to search within that site to find the specific information required
for a given lesson. Please note that information published on the Internet changes over time,
therefore the links provided may no longer contain the specific information related to a given
lesson. Teachers are advised to preview all sites before using them with students.
For the teacher: overhead transparency, a collection of various types of graphs
For the students: chart paper, markers, various sizes of grid paper, math journal
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Group Graphing – Grade Four
Vocabulary:
 bar graph
 line graph
 picture graph
Technology Connection:
Create graphs using graphing software on the computer.
Research Connections:
Daniels, Harvey and Marilyn Bizar. Methods that Matter: Six Structures for Best Practice
Classrooms. Me: Stenhouse Publishers, 2000.
Marzano, Robert J., Jane E. Pollock and Debra Pickering. Classroom Instruction that Works:
Research-Based Strategies for Increasing Student Achievement, Alexandria, Va: Association for
Supervision and Curriculum Development, 2001.
Attachments:
Attachment A, Selection of Best Graph Post-Assessment Rubric
Attachment B, Three Untitled Graphs
Attachment C, Learning About Types of Graphs
Attachment D, Exit Card
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Group Graphing – Grade Four
Attachment A
Selection of Best Graph Post-Assessment Rubric
Exemplary Solution
Complete Solution
Adequate Solution
Inadequate Solution
Choice of graph
for most
appropriate
Appropriate graph
chosen and detailed
explanation given
including several
reasons
Appropriate graph
chosen and
explanation given
with reasons.
Appropriate graph
chosen with limited
explanations.
Inappropriate graph chosen OR no
explanation for appropriate graph.
Choice of graph
for least
appropriate
Appropriate graph
chosen and detailed
explanation given
including several
reasons.
Appropriate graph
chosen and
explanation given
with reasons.
Appropriate graph
chosen with limited
explanations.
Inappropriate graph chosen OR no
explanation for appropriate graph.
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Group Graphing – Grade Four
Attachment B
Three Untitled Graphs
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Group Graphing – Grade Four
Attachment C
Learning About Types of Graphs
Bar Graphs
Line Graphs
Pictographs
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Group Graphing – Grade Four
Attachment D
Exit Card
Your Name ____________________________
Group Members__________________________________________________________
Task
Completed
Still to do
Tomorrow
Questions or Comments About the
Task
Select survey
question.
Collect data.
Organize data into a
chart.
Make bar graph.
Make line graph.
Make picture graph.
Write 3 to 4
interpretation
questions.
Other questions or concerns from the group_____________________________________
________________________________________________________________________
________________________________________________________________________
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